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We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a CouetteTaylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as goes to infinity. This explains rigorously some experiments.
We consider a 2D mathematical model describing the motion of a
solution of surfactants submitted to a high shear stress in a
Couette-Taylor system. We are interested in a stabilization process
obtained thanks to the shear. We prove that, if the shear stress is
large enough, there exists global in time solution for small
initial data and that the solution
of the linearized system (controlled by a nonconstant parameter) tends
to 0 as t goes to infinity. This
explains rigorously some experiments.
...
A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...
Plant growth occurs due to cell proliferation in the meristem. We model the case of
apical meristem specific for branch growth and the case of basal meristem specific for
bulbous plants and grass. In the case of apical growth, our model allows us to describe
the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the
case of basal growth, the spatial structure, which corresponds to the appearance of
leaves, results...
This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain case. Our...
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